A formulation of time-domain FEM for room acoustic simulations with frequency-dependent locally-reacting impedance boundary

A room acoustic simulator using time-domain finite element method (TD-FEM) has been broadened its applicable range as a room acoustic design tool, recently. In the acoustic TD-FEM, constructing various sound absorber model is of crucial importance to perform reliable simulations. However, an accurate time-domain extended-reacting sound absorber model, which can take account for both frequency and incident angle dependence of sound absorption characteristics, has not been developed sufficiently due to the difficulties of modeling. The major difficulty is how to reflect frequency-dependent absorption characteristics efficiently in time-domain because its direct incorporation involves a convolution computation. In the present paper, a recently proposed auxiliary differential equations (ADE) method is applied to model the frequency-dependent locally-reacting impedance boundaries as a preliminary of constructing efficient extended-reacting model. The ADE method can reflect frequency-dependent behaviors in time-domain efficiently by solving additional first-order differential equations instead of the convolution computation. Numerical impedance tube problems demonstrate that the present TD-FEM can accurately simulate broadband absorption characteristics of various porous absorbers up to 10 kHz.